Organism-Scale Modeling of Early Drosophila Patterning via Bone Morphogenetic Proteins  David M. Umulis, Osamu Shimmi, Michael B. O'Connor, Hans G. Othmer  Developmental Cell  Volume 18, Issue 2, Pages 260-274 (February 2010) DOI: 10.1016/j.devcel.2010.01.006 Copyright © 2010 Elsevier Inc. Terms and Conditions

Developmental Cell 2010 18, 260-274DOI: (10.1016/j.devcel.2010.01.006) Copyright © 2010 Elsevier Inc. Terms and Conditions

Figure 1 Introduction and Background (A) Axes and geometry of a Drosophila blastoderm embryo. (B) Schematic of the BMP DV patterning network (cross-section view; legend at the bottom of the figure). Note the “?” on the diagram for the positive feedback, which is still unknown. (C) Alternative positive-feedback mechanisms for signal-induced regulation of extracellular BMPs. (+rec), positive feedback of receptor levels; (+/−end), positive and negative regulation of endocytosis; (-koff), feedback inhibition of ligand release from receptor; (+/−tld), positive and negative regulation of Tld processing; (+cooperativity), positive regulation of type I/II/Dpp-Scw complex formation. (D) Schematic of ligand-inhibitor complex formation in solution and after attached to collagen. Developmental Cell 2010 18, 260-274DOI: (10.1016/j.devcel.2010.01.006) Copyright © 2010 Elsevier Inc. Terms and Conditions

Figure 2 Workflow for the Development of a Data-Driven, Organism-Scale Model Mechanism(s), prepatterns, and geometry are implemented into a 3D geometric representation of the Drosophila blastoderm embryo. Each model simulation gives the distribution of all secreted proteins and complexes along all axes of the embryo. The model's results are compared against the population mean distributions for pMad signaling in wt and eight additional mutants used for the model training. Each mechanism is optimized by comparing the predictions against image data, and alternative mechanisms can then be ranked based on their distance between the best fit and the actual image data. Developmental Cell 2010 18, 260-274DOI: (10.1016/j.devcel.2010.01.006) Copyright © 2010 Elsevier Inc. Terms and Conditions

Figure 3 pMad Variability and Population Statistics (A) Normalized wt pMad level versus position y/Lx at the cross-section x/Lx = 0.5. Lx is the mean length of the AP axis. Red dots are the normalized concentration, the solid blue line is the mean pMad in the cross-section, and the error bars correspond to ±σ. (B) Composite pMad distribution for (beginning at top left) D. melanogaster wt (n = 15), scw+/− (n = 12), sog+/− (n = 9), and tsg+/− (n = 18). (C) Mean coefficient of variation for pMad width averaged along the AP axis for wt as a function of threshold (CV = σ/w: standard deviation/width). Error bars (standard deviation of CV) provide a measure of CV variability along the AP axis. (D) Mean pMad distribution along a cross-section at x/Lx = 0.5. (E and F) Mean width of pMad varies along the AP axis. Thin lines represent the average width for the respective embryos (see legend in the upper-left portion of the figure). Colored data points are superimposed over the lines for the mean width in regions at which the null hypothesis (mean widths between the mutant and wt are equal) is rejected with α = 0.05. Threshold values: (E) T = 0.2 and (F) T = 0.4. Developmental Cell 2010 18, 260-274DOI: (10.1016/j.devcel.2010.01.006) Copyright © 2010 Elsevier Inc. Terms and Conditions

Figure 4 Mechanism Comparison (A) Prepattern distributions as they appear in the 3D model. The Tld distribution and Sog secretion distribution were determined by fluorescent in situ hybridization of tld and sog mRNA (method described in [Lecuyer et al., 2007]). The Bicoid distribution was determined by solving a simple reaction-diffusion equation in the periphery of the embryo (Umulis et al., 2008). (B and C) Box-and-whisker plots of minimum of CV (rmsd/μ) found in the full 3D model for different feedback mechanisms. 50% of all solutions fall within the boxed areas, whereas the whiskers encompass all values within ∼2.7 standard deviations of the mean. (B) Contributions of Tkv and Tld nonuniform distributions; (C) embryo shape. The upper and lower limits of the box represent the upper and lower quartile, respectively, and the red line is the median CV(rmsd) value for the series of embryos tested. In (B), the cases compared are: no positive feedback, positive feedback of receptors, negative and positive feedback on endocytosis rates, positive and negative feedback of Tld processing, positive feedback of a BMP-binding nonreceptor, feedback inhibition of ligand release from receptors, and enhanced formation of ligand-type I/II receptor complexes (Wang and Ferguson, 2005; Umulis et al., 2006). In (B), all models were solved with uniform levels of Tkv and Tld. (C) Case 1: uniform Tkv and Tld, Case 2: uniform Tld, nonuniform Tkv, Case 3: uniform Tkv, nonuniform Tld, and Case 4: nonuniform Tld, nonuniform Tkv for the real embryo geometry (first four) and ellipse approximation of embryo geometry. (D) Typical residual result for the difference between the model result and the mean pMad distribution. (E) BMP-bound receptor levels begin broad and low and contract in time to produce the nonuniform distribution of occupied receptors. (F) BR levels at x/Lx = 0.5. Developmental Cell 2010 18, 260-274DOI: (10.1016/j.devcel.2010.01.006) Copyright © 2010 Elsevier Inc. Terms and Conditions

Figure 5 Role for Type IV Collagen in Regulating the Kinetics of BMP-Mediated Patterning of the Dorsal Surface (A) Decreasing the diffusion coefficients of Sog and Dpp-Scw by 10%–20% decreases the rmsd/μ, but large reductions in the diffusion coefficients lead to progressively higher rmsd/μ values. Inset: model results for the model that includes collagen-mediated formation of Sog/Dpp-Scw complexes. Kinetics are kept constant in (A), and diffusion parameters are kept constant in (B). See the Supplemental Information for parameter values. (B) rmsd/μ versus the forward binding rate for Dpp-Scw + Sog/Tsg in the original model given by Equations 1–7 (·) or Dpp-Scw + Sog in the modified model (+) (Equations 85–91 in the Supplemental Information). The vertical green, shaded region corresponds to the measured dissociation constant for Chordin + BMP-2. The blue, shaded region depicts the diffusion-limited regime for dimerization in solution, and the red, shaded region gives an approximate range for acceptable binding parameters. Developmental Cell 2010 18, 260-274DOI: (10.1016/j.devcel.2010.01.006) Copyright © 2010 Elsevier Inc. Terms and Conditions

Figure 6 3D Model Results (A–S′) (A–S) Mean pMad staining for ectopic gene expression experiments and/or mutant alleles. (A′–S′) Levels of BR calculated by using the computational model. See Section 3 of the Supplemental Information and Figure S8 for additional discussion of the tld7M89 allele. Developmental Cell 2010 18, 260-274DOI: (10.1016/j.devcel.2010.01.006) Copyright © 2010 Elsevier Inc. Terms and Conditions

Figure 7 Mechanisms of Morphogen Scale Invarience-Calculated BR Levels for D. virilis and D. busckii and Predicted Distribution for Embryos 750 μm in Length (A–C′) (A–C) The expected BR levels when conservation conditions are imposed for the total amounts of protein production, and/or protein levels, are shown. (A′–C′) Same as (A)–(C), except without conservation on the total amount of production/proteins in the system (i.e., the concentrations are constant). (D and E) Distribution of pMad signaling in (D) D. busckii (n = 14) and (E) D. virilis (n = 18). (F) Average pMad width along the AP axis is constant between species. (G) Scale invariance does not occur at all positions along the AP axis because the shape of the pMad distribution is different between species. Developmental Cell 2010 18, 260-274DOI: (10.1016/j.devcel.2010.01.006) Copyright © 2010 Elsevier Inc. Terms and Conditions

Figure 8 Predicted Relationship between Model-Predicted Distribution of BR and Different Embryo Shapes (A and B) For each simulation, the mRNA prepattern information was scaled in proportion to the embryo shape changes. Developmental Cell 2010 18, 260-274DOI: (10.1016/j.devcel.2010.01.006) Copyright © 2010 Elsevier Inc. Terms and Conditions